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general topography in his imagination. The method of \Veier-
strass was arithmetical, that of Riemann geometrical and intui-
tive. To say that one is 'better' than the other is meaningless;
both cannot be seen from a common point of view.
Overwork and lack of reasonable comforts brought on a
nervous breakdown early in his thirty-first year, and Riemann
was forced to spend a few weeks with a friend in the Harz
mountain country, where he was joined by Dedekind. The three
took long tramps together into the mountains and Riemann
soon recovered. Relieved of the strain of having to keep up
academic appearances, Riemann indulged his sense of humour
and kept his companions amused with his spontaneous wit.
They also talked shop together - most mathematicians do when
they get together, just as lawyers or doctors or business men do,
provided they do not have to talk drivel to maintain the social
conventions. One evening after a strenuous hike Riemann
dipped into Brewster's life of Newton and discovered the letter
to Bentley in which Newton himself asserts the impossibility
of action at a distance without intervening media. This de-
lighted Riemann and inspired him to an impromptu lecture.
To-day the 'medium' which Riemann extolled is not the lumini-
ferous ether, but his own 'curved space', or its reflexion in the
space-time of relativity.
At last, in 1857, at the age of thirty-one, Riemann got his
assistant professorship. His salary was the equivalent of about
300 dollars a year, but as he had had little all his life he missed
less. However, a real disaster presently descended on him: his
brother died and the care of three sisters fell to his lot* It
figured out at exactly seventy-five dollars a year for each of
them. Love on nothing a year in a cottage may be paradise;
existence on next to nothing in a university community is just
plain hell. It was but little different hi Riemann's day. No
wonder he contracted consumption. However, the Lord, who
had so generously given, shortly relieved Riemann of his
youngest sister, Marie, so the individual budgets skyrocketed
to 100 dollars a year. If rations had to be watched, affection was
free, and Riemann was more than repaid for his sacrifices by the
self-confidence inspired in him by his sisters' devotion and